The last Ice Age didn't last for 1000 years. It is known as the
Quaternary glaciation (or Pleistocene glaciation).
It began around 2.5 million years ago, hence at the start of Quaternary period and the Pleistocene epoch. This last Ice Age had a number or cycles of glacial and interglacial periods.
Interglacial period is a period of warm climate, that can last for thousands of years, in between two glacial periods.
Meaning the ice age goes through series of cold and warm stages, and each stage last for 10s or 100s of years.
The Holocene epoch marked the end of the very last glacial period, about 10,000 or 11,000 years ago, when the Neolithic period started.
Some palaeo-climate experts or scientists, think that the Ice Age hasn't ended yet; that our current epoch - the Holocene - is merely interglacial period. That another glacial period might occur sometimes in the next few thousand years from now, but that's only a prediction, not a certainty.
Despite the terms "Ice Age", it is common mistake for most people who never study the last Ice Age that the whole earth was covered in ice. That's not true.
The ice sheets only covered certain region. Much of the lands of lower attitudes was untouched by ice sheets.
In the New World, the ice-sheets covered all of Canada, but only certain regions in the US. In the south, only the the Andes mountain range were covered.
And in the Euroasian continent it mostly covered the British Isles, Scandinavia, parts of Central Europe and Siberia. Pockets of ice sheets covered highlands, such as the Swiss Alps and the Himalayas.
Can you provide a scientific sources that say the Ice Age only lasted for 1000 years?